checkpoints aren't too bad on the 10. if you're coming from the east you may see one an hour or two before el paso and one after el paso, about 20-30 miles deep into new mexico. there is no checkpoint for the nm/az state line unless they're trying to get tricky that day. tombstone likes to put up random checkpoints every so often, but thats not on the interstate and mainly around holidays looking for illegals traveling to see their families and what not.
chances are they'll just look at you and ask you if you're an american citizen when you go through one.

safe travels.